Hello daviddweb,
Thanks for reaching out!
At the moment the date field is not available in the additional fields. The only field types available are text, radio button, checkbox and dropdown list.
If you think that is something you would like as a feature I encourage you to visit our User Voice Page and either upvote an existing request or make a new request there.
It might be possible to do this but would require customization work, which we are limited to support. Here is a list of developers though, who might be able to help you out with this. They are well known names in the community and are not affiliated with us.
https://theeventscalendar.com/knowledgebase/find-a-customizer/
Let me know if this answers your question or if you have another one.
Thanks and cheers,
Andras